"All such problems can be formulated as mathematical programming problems. Naturally, we can propose many sophisticated algorithms and a theory but the final test of a theory is its capacity to solve the problems which originated it." (George B Dantzig, "Linear Programming and Extensions", 1963)
"If the system exhibits a structure which can be represented by a mathematical equivalent, called a mathematical model, and if the objective can be also so quantified, then some computational method may be evolved for choosing the best schedule of actions among alternatives. Such use of mathematical models is termed mathematical programming." (George B Dantzig, "Linear Programming and Extensions", 1963)
"Linear programming is viewed as a revolutionary development giving man the ability to state general objectives and to find, by means of the simplex method, optimal policy decisions for a broad class of practical decision problems of great complexity. In the real world, planning tends to be ad hoc because of the many special-interest groups with their multiple objectives." (George B Dantzig, "Mathematical Programming: The state of the art", 1983)
"Linear programming and its generalization, mathematical programming, can be viewed as part of a great revolutionary development that has given mankind the ability to state general goals and lay out a path of detailed decisions to be taken in order to 'best' achieve these goals when faced with practical situations of great complexity. The tools for accomplishing this are the models that formulate real-world problems in detailed mathematical terms, the algorithms that solve the models, and the software that execute the algorithms on computers based on the mathematical theory." (George B Dantzig & Mukund N Thapa, "Linear Programming" Vol I, 1997)
"Linear programming is concerned with the maximization or minimization of a linear objective function in many variables subject to linear equality and inequality constraints." (George B Dantzig & Mukund N Thapa, "Linear Programming" Vol I, 1997)
"Mathematical programming (or optimization theory) is that branch of mathematics dealing with techniques for maximizing or minimizing an objective function subject to linear, nonlinear, and integer constraints on the variables." (George B Dantzig & Mukund N Thapa, "Linear Programming" Vol I, 1997)
"Models of the real world are not always easy to formulate because of the richness, variety, and ambiguity that exists in the real world or because of our ambiguous understanding of it." (George B Dantzig & Mukund N Thapa, "Linear Programming" Vol I, 1997)
"The linear programming problem is to determine the values of the variables of the system that (a) are nonnegative or satisfy certain bounds, (b) satisfy a system of linear constraints, and (c) minimize or maximize a linear form in the variables called an objective." (George B Dantzig & Mukund N Thapa, "Linear Programming" Vol I, 1997)
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